Can an evolutionary algorithm adapt to a changing environment?
The core question to whether or not an AI is adaptable or not is whether or not it supports online learning. That doesn't mean using the Internet to learn things; that means continuing to accept training data during the functioning of the system.

This is (mostly) independent of the underlying architecture; in evolutionary approaches one can continue to breed generations with a shifting fitness function or with neural networks one can continue to backpropagate errors, and so on with other approaches.